In this work we deal with global stability properties of classic SIS, SIR and SIRS epidemic models with constant recruitment rate, mass action incidence and variable population size. The usual approach to determine global stability of equilibria is the direct Lyapunov method which requires the construction of a function with specific properties. In this work we construct different Lyapunov func...

This paper studies the iteration-complexity of new regularized hybrid proximal extragradient (HPE)-type methods for solving monotone inclusion problems (MIPs). The new (regularized HPE-type) methods essentially consist of instances of the standard HPE method applied to regularizations of the original MIP. It is shown that its pointwise iteration-complexity considerably improves the one of the H...

Linear interpolation requires a single multiplication but is signiicantly less accurate than quadratic interpolation. The latter requires two multiplications. Two novel quadratic interpolation schemes are shown here that approximate the functions required by the Logarithmic Number System (LNS) with more accuracy than linear interpolation using only a single multiplication. One method uses two R...

Under the strongly convex assumption, several recent works studied the global linear convergence rate of the proximal incremental aggregated gradient (PIAG) method for minimizing the sum of a large number of smooth component functions and a non-smooth convex function. In this paper, under the quadratic growth condition–a strictly weaker condition than the strongly convex assumption, we derive a...

In this work, we explain a new numerical schemes of collocation methods based on the adapted quadratic approximation of singular integral with logarithmic kernel. This approximation leads to obtain the numerical solution of singular integral equations with logarithmic kernel on an oriented smooth contour.

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...

We propose an efficient computational method for linearly constrained quadratic optimization problems (QOPs) with complementarity constraints based on their Lagrangian and doubly nonnegative (DNN) relaxation and first-order algorithms. The simplified Lagrangian-CPP relaxation of such QOPs proposed by Arima, Kim, and Kojima in 2012 takes one of the simplest forms, an unconstrained conic linear o...

In this article, we aim to solve high-dimensional convex quadratic programming (QP) problems with a large number of terms, linear equality, and inequality constraints. To the targeted QP problem desired accuracy efficiently, consider restricted-Wolfe dual develop two-phase Proximal Augmented Lagrangian method (QPPAL), Phase I generate reasonably good initial point warm start II obtain an accura...

In this article we present a version of the proximal alternating direction method for a convex problem with linear constraints and a separable objective function, in which the standard quadratic regularizing term is replaced with an interior proximal metric for those variables that are required to satisfy some additional convex constraints. Moreover, the proposed method has the advantage that t...